Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
500 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11731787 | C2 | semidirect |
| 4. #11725461 | C2 | semidirect |
| 5. #11725440 | C2 | semidirect |
| 239. C7 | #10351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11731787 | 2 |
| C7×#1957 | 2 |
| #11729515 | 2 |
| #11725461 | 2 |
| #11725440 | 2 |
| #10351 | 7 |